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Where is the glitch?

1. Let a single free electron move along x axis with constant speed Vx. It encounters magnetic field on its right side, so the Lorentz force accelerates it along y axis and it gains speed Vy.

--- Glitch or pass?

2. The electron does not slow down in x direction when it starts accelerating in y direction, but instead this new gained speed in y direction adds up to its Vx velocity vector, increases its speed and kinetic energy along with changing its trajectory.

--- Glitch or pass?

x direction of wire1 electrons drift

y direction of wire2 B field

z direction of Lorentz force acting on wire1 electrons

Direction of wire1 electrons displacement due to Lorentz force is in z direction downwards, the same direction Lorentz force is pointing to.

--- Glitch or pass?

{0,0,1} dot {1,0,0} = 0 <- drift velocity vector = wrong displacement vector

{0,0,1} dot {0,0,1} = 1 <- acceleration/displacement vector = correct vector

1. Let a single free electron move along x axis with constant speed Vx. It encounters magnetic field on its right side, so the Lorentz force accelerates it along y axis and it gains speed Vy.

--- Glitch or pass?

2. The electron does not slow down in x direction when it starts accelerating in y direction, but instead this new gained speed in y direction adds up to its Vx velocity vector, increases its speed and kinetic energy along with changing its trajectory.

--- Glitch or pass?

x direction of wire1 electrons drift

y direction of wire2 B field

z direction of Lorentz force acting on wire1 electrons

Direction of wire1 electrons displacement due to Lorentz force is in z direction downwards, the same direction Lorentz force is pointing to.

--- Glitch or pass?

Please mark your axis and be specific about your directions. That vdt is wrong velocity vector, electrons drift vector. That is not the displacement in the direction of the force. Acceleration, velocity and the displacement due to Lorentz force are all vectors pointing where the Lorentz force is pointing itself, that's given by F= ma.Here I use only the definition of work and the expression for the magnetic force:

[tex]

W = \int_{t_1}^{t_2} \mathbf{F_\mathbf{mag}} \cdot \mathbf{v} \, \mathrm{d}t = \int_{t_1}^{t_2} \left( q \mathbf{v} \times \mathbf{B} \right) \cdot \mathbf{v} \, \mathrm{d}t = \int_{t_1}^{t_2} 0 \, \mathrm{d}t = 0

[/tex]

It's a very simple equation. You're saying this is somehow wrong?

{0,0,1} dot {1,0,0} = 0 <- drift velocity vector = wrong displacement vector

{0,0,1} dot {0,0,1} = 1 <- acceleration/displacement vector = correct vector

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